Evaluation leaderboards such as LMArena play a central role in benchmarking large language models by aggregating pairwise human preferences into model rankings, yet the robustness of these rankings remains poorly understood. We present a unified perturbation framework for analyzing Bradley-Terry leaderboards under structured data modifications using influence-based approximations. Our framework studies three match-level perturbations -- Drop, Add, and Flip -- together with player removal, and evaluates their effects on top-k membership, global ranking consistency via Kendall's tau, and confidence-interval-based uncertainty. Across Chatbot Arena and six additional pairwise-comparison datasets, we show that modern leaderboards are non-robust across all three objectives: sub-1% targeted perturbations can change the top-ranked model, degrade Kendall's tau, and alter confidence intervals. Beyond robustness auditing, we show that the same influence scores enable efficient targeted perturbations, promoting or demoting specific models and reducing target-model uncertainty with fewer actions than previous manipulation and active-sampling baselines. By summarizing these effects with normalized dataset-level robustness scores, our framework provides a practical and helpful tool for auditing leaderboard stability and motivating more robust evaluation protocols.
We propose a method for evaluating the robustness of widely used LLM ranking systems -- variants of a Bradley--Terry model -- to dropping a worst-case very small fraction of preference data. Our approach is computationally fast and easy to adopt. When we apply our method to matchups from popular LLM ranking platforms, including Chatbot Arena and derivatives, we find that the rankings of top-performing models can be remarkably sensitive to the removal of a small fraction of preferences; for instance, dropping just 0.003% of human preferences can change the top-ranked model on Chatbot Arena. Our robustness check identifies the specific preferences most responsible for such ranking flips, allowing for inspection of these influential preferences. We observe that the rankings derived from MT-bench preferences are notably more robust than those from Chatbot Arena, likely due to MT-bench's use of expert annotators and carefully constructed prompts. Finally, we find that neither rankings based on crowdsourced human evaluations nor those based on LLM-as-a-judge preferences are systematically more sensitive than the other.
Pretrained models are often evaluated on multi-task leaderboards to measure their applicability in diverse contexts. However, current methods for aggregating performance across tasks into leaderboard-level rankings do not address the uncertainty and variability at the task level. While recent works have proposed interval-based model rankings, the principled aggregation of uncertainty from individual tasks to leaderboard-level rankings remains unaddressed, and variation in models' performance across tasks is frequently obscured. In this work, we introduce a hierarchical framework that constructs model rank intervals with statistical guarantees at both levels: task-level rank confidence intervals from pairwise comparisons, and leaderboard-level rank prediction intervals using a conformal approach. This enables reliable quantification of model rank for each observed task and for new potential tasks. Experiments on simulated data and the TabArena and PromptEval (MMLU) benchmarks show that our method yields statistically valid and informative intervals, enabling reliable, uncertainty-aware model ranking on leaderboards.
Multi-task benchmarks have become a central pillar of machine learning research, yet their growing influence has incentivised benchmark gaming -- strategic actions taken to improve the leaderboard rank of a specific model. Treating datasets as voters and models as candidates, we consider benchmark-specific training -- the inclusion of benchmark data in training -- as a form of election manipulation. For any ordinal benchmark, the problem of choosing datasets to train on so that a target model becomes top-ranked corresponds to shift bribery, a class of manipulation problems from computational social choice. Leveraging this identification, we show that the benchmark-specific training problem is NP-hard under Borda count and mean win rate. Complementing this worst-case perspective, we introduce the instance-level robustness, the minimum number of datasets a model developer must include in training to top a given leaderboard, and derive expressions for it under arithmetic mean, median, mean win rate and pairwise majority. We evaluate these expressions on MMLU under HELM and on BIG-Bench Hard (BBH) under the Open LLM Leaderboard. Across both suites, mean win rate is hardest to manipulate: this gap is clear on BBH (24 tasks, 4507 models), where its median robustness is 22 tasks (92%), compared with 13 (54%) under arithmetic mean and 12 (50%) under median and pairwise majority.
Polina Gordienko, Georg Schollmeyer, Frauke Kreuter +1